Abstract
The present study proposes two alternate model structures to represent
exponentially damped sinusoids and proposes a novel method of estimating
the parameters of the damped sinusoids by combining Hankel singular
value decomposition (HSVD) with the extended complex Kalman filter
(ECKF). The ECKF is capable of estimating the parameters and can
effectively track the variations of damping constants and frequencies.
However, the performance of ECKF has been found to be very sensitive
to initial state estimates when one of the proposed model (called
model-1) is used for representing the signal. Some of the existing
methods of damped signal estimation including HSVD, which belong
to the class of batch processing algorithms, are not sensitive to
initial conditions. However, these are unsuitable for tracking variations
of signal parameters. The proposed algorithm, therefore, uses HSVD
to accurately estimate the initial states from few samples of the
signal. These estimates are subsequently being used by ECKF to eliminate
its sensitivity to initial conditions. The structure of Model-1 is
further modified to yield another model structure (called Model-2)
to represent the damped signal. The parameters of the damped signal
were estimated under variety of noisy conditions by ECKF using both
Model-1 amp; 2. Their effectiveness were compared by computing the
the variances of estimates and comparing those with Cramer-Rao (CR)
bound. Results of estimation show that Model-2 is more efficient
compared to Model-1 and ECKF is capable of accurately tracking the
variations in signal parameters.
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